Peel and grate, roughly, the carrots. Then, melt about 3 or 4 Tbsp olive oil in a heavy bottomed pan, and when it is hot, add a chopped onion. Cook the onion slowly and gently, until it becomes soft and smells delicious. A little browning of its edges will do no harm.
Dump in the carrots. Stir them and salt them lightly to extract some water from them -- vegetables that are "etuveed" steam mostly in their own juices.
Cover the pot with a lid, and then add a little nutmeg (1/4 tsp), lemon juice (about 1 Tbsp), butter (think generously -- 2 to 4 Tbsp), and a splash of white wine -- perhaps 1/4 cup at most. Cover and cook all this gently for about 20 minutes, until the carrots have absorbed all the seasonings, wine, and butter, and are soft and delicious. Sprinkle some parsley over them at the last minute.
Any white wine is good for this recipe, but chardonnay seems especially appropriate. Madeleine suggests the wine might be replaced with apple cider, too, which is something I have not tried yet.
You want these carrots, the next time you have a roast chicken or any white meat, including pork, veal, or fish. Trust me (and Madeleine). You want them.